Thanks Francois, that's exactly what I wanted to know. Except for the NURBs.
If anyone knows the Equations for NURBS, I'd be very grateful.

Thanks,

Nekar Xenos

Francois Labreque <fla### [at] videotronca> wrote in message
news:3A683D50.644E85D5@videotron.ca...
>
>
> J-Print News wrote:
> >
> > I've been waiting for replies and it seems I posted this message to Warp
> > instead of the board. Sorry about that, Warp.
> >
> > That's equations I'm looking for, not functions. Stuff like y=mx^2 +c,
etc.
> > I'm not so good on the terminology. Equations to work out the x, y, and
z
> > coordinates for Beziers, NURBS and isosurfaces is what I want. I've
never
> > heard of 3d beziers but I don't think that should be impossible.
>
> Bezier curves use a set of control points that act like magnets on a
> piece of metallic string.  Points on the curve are defined by the
> following equation (For n+1 control points):
>
> [use a fixed-sized font]
>
>         n
>        ---
>        \
> P(u) = / Pi Bi,n(u)  0<= u <=1
>        ---
>        i=0
>
> Where Pi is a control point and Bi,n(u) is the Berstein polynomial,
> which is given by:
>
>                   i     n-i
> Bi,n (u) = C(n,i)u (1-u)
>
> where C(n,i) is a coefficient given by:
>
>             n!
> C(n,i) = -------
>          i!(n-i)!
>
>
> [Ref: I. Zeid, CAD/CAM Theory and Practice, 1991. McGraw-Hill]
>
> I don't know how NURBS work, but you should be able to find that out in
> a book on computer algorithms at your local (or college) library.
>
> And isosurfaces are any equation you want, anything is possible.
>
> > PS. Does anyone know the equation for the Mandelbrot pattern. I think
it's
> > something like y=mX+c with c being the sqare root of -1 but I can't
remember
> > how it is used.
>
> It's an infinite loop.
>
> Zn = Z(n-1)^2 + c
>
> Where Zo is 0 and C the point (in the complex plane) whose colour you
> want to find out.  If, after n iterations, you are converging towards 0,
> the point is inside the Mandelbrot set; on the other hand if you are
> diverging towards infinity, you are outside of it.  Usually
> image-generating programs will assign a color to the pixel based on how
> many iterations it took before the point gets outside a threshold (for
> the regular "ladybug" Mandelbrot set, it's a circle of radius 2)
>
> [Ref: T. wegner & B. Tyler, Fractal Creations, 2nd ed. 1994, Waite
> Group]
>
> Hope this helps.
> --
> Francois Labreque | In the future, performance will be measured
>     flabreque     | by the size of your pipe.
>         @         |             - Dogbert, on networking
>    videotron.ca

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